Download 2.4 Practice with Examples

LESSON
2.4
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 96–101
GOAL
Use properties from algebra and use properties of length and
measure to justify segment and angle relationships
VOCABULARY
Algebraic Properties of Equality
Let a, b, and c be real numbers.
Addition Property If a b, then a c b c.
Subtraction Property If a b, then a c b c.
Multiplication Property If a b, then ac bc.
Division Property If a b and c 0, then a c b c.
Reflexive Property For any real number a, a a.
Symmetric Property
If a b, then b a.
Transitive Property If a b and b c, then a c.
Substitution Property If a b, then a can be substituted for b in any
equation or expression.
Chapter 2
EXAMPLE 1
Writing Reasons
Solve 10 2x 3x 2 4 and write a reason for each step.
SOLUTION
10 2x 3x 2 4
Given
10 2x 3x 6 4
Distributive property
10 2x 3x 2
Simplify.
12 2x 3x
Addition property of equality
12 5x
Addition property of equality
12
x
5
Division property of equality
Copyright © McDougal Littell Inc.
All rights reserved.
Geometry
Practice Workbook with Examples
31
LESSON
2.4
CONTINUED
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 96–101
Exercises for Example 1
Chapter 2
Solve the equation and write a reason for each step.
EXAMPLE 2
1. 2x 3 7x
2. 4 23x 5 11 x
3. 6x 2 4x 1
4.
3
1
x 4 2x 5
5
Using Properties of Length and Measure
In the diagram, WY XZ,
show that WX YZ.
W
X
Y
Z
SOLUTION
32
WY XZ
Given
WY WX XY
Segment Addition Postulate
XZ XY XZ
Segment Addition Postulate
WX XY XY YZ
Substitution property of equality
WX YZ
Subtraction property of equality
Geometry
Practice Workbook with Examples
Copyright © McDougal Littell Inc.
All rights reserved.
LESSON
2.4
CONTINUED
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 96–101
Exercises for Example 2
Use the given information to show the desired statement.
5. Given that MN PQ,
6. Given that AB DE and BC CD,
show that MP NQ.
show that AD BE.
M
D
E
C
N
A
B
P
Q
show that mAQC mBQD.
Chapter 2
7. Given that mAQB mCQD,
8. Given that mRPS mTPV and
mTPV mSPT, show that
mRPV 3mRPS
A
B
R
C
Q
D
S
P
T
V
Copyright © McDougal Littell Inc.
All rights reserved.
Geometry
Practice Workbook with Examples
33